The use of cells of fibrous material to coalesce dispersed oil droplets in a water emulsion is a known procedure, particularly in the petroleum industry. In a typical cell for this purpose the emulsion is passed through one or more layers of fibrous material having the characteristic that oil droplets cling to the fibrous material while water passes more freely, the oil droplets growing in size as they are contacted by other oil droplets until the size of the oil droplets become such that the flow of fluid breaks the surface tension between the fibrous material and the oil droplets, causing the oil droplets to pass to the exterior of the fibrous material. On the exterior surface of the cell the droplets continue to grow in size to form globules and when a globule reaches a size sufficient to overcome surface tension it rises to the surface of the water surrounding the cell where the oil accumulates and is drawn off. Water is withdrawn from the bottom of the cell. As an illustration of a coalescing cell in this manner may be seen by referring to my copending application entitled "Filter Cell Having Catalytic Material Therein" filed concurrently herewith.